The linear displacement x of the bob of a sim | vedclass

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(C) The given equation for displacement is $x = a \sin \left(\frac{\pi}{\sqrt{2}} t\right)$.Comparing this with the standard $SHM$ equation $x = a \si

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(C) The given equation for displacement is $x = a \sin \left(\frac{\pi}{\sqrt{2}} t\right)$.Comparing this with the standard $SHM$ equation $x = a \sin(\omega t)$,we get the angular frequency $\omega = \frac{\pi}{\sqrt{2}} \ rad/s$.The time period $T$ is given by $T = \frac{2\pi}{\omega} = \frac{2\pi}{\pi/\sqrt{2}} = 2\sqrt{2} \ s$.The formula for the time period of a simple pendulum is $T = 2\pi \sqrt{\frac{\ell}{g}}$.Squaring both sides,we get $T^{2} = 4\pi^{2} \frac{\ell}{g}$.Substituting $T = 2\sqrt{2}$ and $g = \pi^{2}$,we have $(2\sqrt{2})^{2} = 4\pi^{2} \frac{\ell}{\pi^{2}}$.$8 = 4\ell$.Therefore,$\ell = 2 \ m$.

The linear displacement $x$ of the bob of a simple pendulum from its mean position varies as $x = a \sin \left(\frac{\pi}{\sqrt{2}} t\right)$,where $a$ is its amplitude expressed in meters and $t$ is in seconds. The length of the simple pendulum is (Take $g = \pi^{2} \ m/s^{2}$): (in $m$)

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